Phase structure of Causal Dynamical Triangulations in 4D

Causal Dynamical Triangulations (CDT) is a lattice approach to quantum gravity. CDT has rich phase structure, including a semiclassical phase consistent with Einstein's general relativity. Some of the observed phase transitions are second (or higher) order which opens a possibility of investigating the ultraviolet continuum limit. Recently a new phase with intriguing geometric properties has been discovered and the new phase transition is also second (or higher) order.Comment: To appear in Acta Physica Polonica B Proceedings Supplement. Presented at the 3rd Conference of the Polish Society on Relativity. 5 pages, 1 figur

Causal Dynamical Triangulations on a torus

Causal Dynamical Triangulations (CDT) is a non-perturbative lattice approach to quantum gravity where one assumes space-time foliation into spatial hyper-surfaces of fixed topology. Most of the previous studies of CDT were done for the fixed spatial topology of the 3-sphere. We present recent results for the fixed spatial topology of the 3-torus. We argue that the topology change does neither affect the phase structure nor the order of the phase transitions. Thus, the CDT properties seem to be universal, independently of the spatial topology choice

Quantum gravity on a torus

Causal Dynamical Triangulations (CDT) is a non-perturbative lattice approach to quantum gravity where one assumes space-time foliation into spatial hyper-surfaces of fixed topology. Most of the CDT results were obtained for the spatial topology of the 3-sphere. It was shown that CDT has rich phase structure, including the semiclassical phase consistent with Einstein's general relativity. Some of the phase transitions were found to be second (or higher) order which makes a possibility of taking continuum limit viable. Here we present new results of changing the spatial topology to that of the 3-torus. We argue that the topology change does not change the phase structure nor the order of the phase transitions. Therefore CDT results seem to be universal independent of the topology chosen.Comment: To appear in Acta Physica Polonica B Proceedings Supplement. Presented at the 6th Conference of the Polish Society on Relativity. 4 pages, 1 figur

Polish jurisprudence in a crooked mirror : (a polemic with Tomasz Bekrycht and Rafał Mańko)

Artykuł zawiera krytykę obrazu dwudziestowiecznej teorii i filozofii prawa, jaki przedstawili Tomasz Bekrycht i Rafał Mańko w artykule pt. Polish Jurisprudence in the 20th Century: A General Overview, opublikowanym na łamach Review of Central and East European Law (2020, nr 45). Argumentujemy, że wskazany artykuł nie jest niewyważony i stronniczy, w związku z czym przedstawia nietrafny obraz polskiej teorii i filozofii prawa

Searching for a continuum limit in causal dynamical triangulation quantum gravity

We search for a continuum limit in the causal dynamical triangulation (CDT) approach to quantum gravity by determining the change in lattice spacing using two independent methods. The two methods yield similar results that may indicate how to tune the relevant couplings in the theory in order to take a continuum limit.Comment: 19 pages, 8 figures. Title change and journal reference adde

Pseudo-Cartesian coordinates in a model of Causal Dynamical Triangulations

Causal Dynamical Triangulations is a non-perturbative quantum gravity model, defined with a lattice cut-off. The model can be viewed as defined with a proper time but with no reference to any three-dimensional spatial background geometry. It has four phases, depending on the parameters (the coupling constants) of the model. The particularly interesting behavior is observed in the so-called de Sitter phase, where the spatial three-volume distribution as a function of proper time has a semi-classical behavior which can be obtained from an effective mini-superspace action. In the case of the three-sphere spatial topology, it has been difficult to extend the effective semi-classical description in terms of proper time and spatial three-volume to include genuine spatial coordinates, partially because of the background independence inherent in the model. However, if the spatial topology is that of a three-torus, it is possible to define a number of new observables that might serve as spatial coordinates as well as new observables related to the winding numbers of the three-dimensional torus. The present paper outlines how to define the observables, and how they can be used in numerical simulations of the model.Comment: 26 pages, 15 figure